KNOXVILLE, Tenn.—"Big Jim" Haslam never imagined the wealth that would be generated from a company he founded with a single gas station bought for $6,000 in 1958.

The empire the 82-year-old patriarch created—Pilot Corp., which operates Pilot Flying J, the largest truck-stop chain in North America—enabled one son, Jimmy, to buy the Cleveland Browns last year, and helped propel the other, Bill, into the governorship of Tennessee in 2011. It financed two buildings and an athletic field at the University of...